Question: Solve for $x$ and $y$ using elimination. ${x-3y = 1}$ ${-2x-5y = -24}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ ${2x-6y = 2}$ $-2x-5y = -24$ Add the top and bottom equations together. $-11y = -22$ $\dfrac{-11y}{{-11}} = \dfrac{-22}{{-11}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x-3y = 1}\thinspace$ to find $x$ ${x - 3}{(2)}{= 1}$ $x-6 = 1$ $x-6{+6} = 1{+6}$ ${x = 7}$ You can also plug ${y = 2}$ into $\thinspace {-2x-5y = -24}\thinspace$ and get the same answer for $x$ : ${-2x - 5}{(2)}{= -24}$ ${x = 7}$